I'm pretty sure this car has open headers or at bare minimum single chamber race mufflers. you can hear the car going lean on decel and backfiring out the pipes. It would probably kill the best of microphones... guy has serious driving skills and big balls. Awesome vid OP!
You're pretty much right. The car most likely has the vintage style Trans Am racing exhaust... consisting of full length headers into large side exit pipes. So, no mufflers at all. I doubt most microphones would be able to shield out that kind of noise/music.